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Related papers: Conformal bootstrap in Liouville Theory

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We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special…

High Energy Physics - Theory · Physics 2016-01-12 Madalena Lemos , Pedro Liendo

A new rigorous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of…

High Energy Physics - Theory · Physics 2009-10-31 Matthias R Gaberdiel , Peter Goddard

We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $\beta \in (0, 8\pi)$, such that the difference of the two fields is a H\"older continuous function. The…

Probability · Mathematics 2025-08-22 Michael Hofstetter , Ofer Zeitouni

Toda Conformal Field Theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras. One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced…

Probability · Mathematics 2024-12-18 Baptiste Cerclé

Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proceeding, we review two aspects of this topic. The first is…

Probability · Mathematics 2025-10-21 Nina Holden , Xin Sun

In the gravitational context, Liouville theory is the two-dimensional conformal field theory that controls the boundary dynamics of asymptotically AdS_3 spacetimes at the classical level. By taking a suitable limit of the coupling constants…

High Energy Physics - Theory · Physics 2015-06-11 Glenn Barnich , Andrés Gomberoff , Hernán A. González

Conformal theories in a d dimensional spacetime may be expressed as manifestly conformal theories in a d+2 dimensional conformal space as first proposed by Dirac. The reduction to d dimensions goes via the d+1 dimensional hypercone in the…

High Energy Physics - Theory · Physics 2007-05-23 Par Arvidsson , Robert Marnelius

We discuss an idea of how 3D critical exponents can be determined by Conformal Field Theory techniques.

High Energy Physics - Theory · Physics 2011-11-10 Slava Rychkov

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward…

High Energy Physics - Theory · Physics 2016-01-27 Christopher Beem , Madalena Lemos , Leonardo Rastelli , Balt C. van Rees

Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument…

High Energy Physics - Theory · Physics 2009-10-28 H. Dorn , H. -J. Otto

Liouville's theorem says that in dimension greater than two, all conformal maps are M\"obius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally…

Differential Geometry · Mathematics 2025-01-07 Ulrich Pinkall , Boris Springborn

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…

High Energy Physics - Theory · Physics 2021-02-24 Justin Kaidi , Eric Perlmutter

In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of…

High Energy Physics - Theory · Physics 2017-08-16 Arjun Bagchi , Mirah Gary , Zodinmawia

Conformal blocks of Liouville theory have a Coulomb-gas representation as Dotsenko-Fateev (DF) integrals over the positions of screening charges. For q-deformed Liouville, the conformal blocks on a sphere with an arbitrary number of…

High Energy Physics - Theory · Physics 2013-11-05 Mina Aganagic , Nathan Haouzi , Can Kozcaz , Shamil Shakirov

The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…

Statistical Mechanics · Physics 2009-11-13 Bruno Carneiro da Cunha

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…

High Energy Physics - Theory · Physics 2024-08-30 Kausik Ghosh , Zechuan Zheng

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…

High Energy Physics - Theory · Physics 2016-09-06 S. Ferrara , C. Fronsdal

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…

High Energy Physics - Theory · Physics 2020-06-10 Stefanos R. Kousvos , Andreas Stergiou

Recent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon expansion and conformal bootstrap calculations. We find…

High Energy Physics - Theory · Physics 2015-06-17 Davide Gaiotto , Dalimil Mazac , Miguel F. Paulos

The symmetry algebra of $N=1$ Super-Liouville field theory in two dimensions is the infinite dimensional $N=1$ superconformal algebra, which allows one to prove, that correlation functions, containing degenerated fields obey some partial…

High Energy Physics - Theory · Physics 2009-10-30 R. Poghossian